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Friday, March 23, 2007

Bohmian Bloom

Carl Brannen appears to have posted nibbles all over the place regarding a new way of looking at the delta parameter in the 3x3 mass matrices, which should bring a smile to the face of the Bohmian mechanics. The nice thing about a good theory is that everybody is happy.

It involves exchanging a classical function $\psi$ for an exponentiated (quantum) version. For us, as always, this is about the profound interaction of addition and multiplication thought of as monads. (This came up recently in our discussion of the Riemann hypothesis).

And for some fun, here is my stylised version of Kuperberg's generalised 6j symbol, from the spider paper. The mushy rectangles are Jones-Wenzl idempotents.

Lastly, degrees of freedom are a bit more than dimensions. From fractal standpoint, the degree of freedom as a dimensional parameter makes little sense, which is why I prefer to discuss Hausdorff dimensions rather than box dimensionality.

Hi all. Doug, it would not be surprising to find concurrency ideas in these categorified knot systematics. And I agree with Mahndisa that conventional 'hidden degrees of freedom' are yucky. Fortunately, as I understand it, this is not at all what Carl is talking about. The usual cheap idea still imagines an objective space on which matter is placed. But here the underlying classical reality is much more subtle: it emerges from the world of measurement as a shared reality between observers. The classical functions that appear must be very, very special...like a zeta function is special.